American Charley Hoffman avoided similar hazards to lead the event at 10-under par.
The ball settled 70 feet away on the fringe, and Hoffman made the putt for a birdie, a 1-under 71 and a share of the lead with Kevin Kisner. Neither could get anything going in the final round, and both shot 73.
The world number three, who had surged through the field thanks to a flawless 65 on Saturday, made the ideal start with a birdie from six feet on the first, but bogeyed the third after finding a water hazard with his approach.
Speaking about the 18th, McIlroy added: "I saw Leishman eagle 16 so I thought I really needed to try and hole it and I was overly aggressive with it and missed the one coming back, but it's been a good week and if anything, to be one over after two rounds and come up like this, it's a great weekend".
"These guys are not afraid and they're going to make a lot of birdies and there's no protecting leads", Kisner said.
"I putted really well all week", Leishman said.
McIlroy then proceeded to knock his birdie attempt past the hole by eight feet, then missed the comebacker, leaving him with a bogey and final-round 3-under 69 that was good enough for a share of fourth place, two behind Leishman, the eventual victor.
It was the first by an Australian on the US PGA Tour this year, and the second this season after Rod Pampling's win in Las Vegas in November.
USMNT roster for March World Cup qualifiers announced
DaMarcus Beasley , who has played in World Cups since 2002, got the call ahead of Greg Garza to provide depth at left back. Michael Orozco and Geoff Cameron are also options, but Johnson is the more natural fit.
Leishman has already been a contender in majors, missing out in a playoff for the 2015 British Open at St Andrews and sharing fourth place when countryman Adam Scott won the Masters green jacket in 2013. Another reason why it's so special this week is this is the first time I've won a tournament with me family here. It bounced off the rocks and into the water, as you can see. "It would have been great if he was up there standing on the back of the green but to win at his place is a dream come true".
"Well, not happy", Kisner said.
He commented: "It's always hard, but we all try to peak for the first week in April at Augusta, and I certainly seem to be trending in the right direction at the moment".
Timing is everything, and, like many other top professionals over the last few years, McIlroy was acutely aware that Palmer was well into the back nine of his celebrated journey through life.
"I have had quite a few chances to win this year". "I want to do well but it makes golf less important".
"Hey, why can't I run out on the green?"
McIlroy and Hatton will be back in action next week at the World Golf Championship Match Play event in Texas.
"I'll go to Augusta, but I'll have to go order (children's) outfits for the Par-3 contest. Ten under for the weekend around here is good scoring, and I can take a lot of positives from it going into next week".